1. Introduction the General Linear Model (GLM) l 2 quantitative variables l 3a  main effects model with no interaction l 3b  interaction model l 2 categorical variables l 4a  main effects model with no interaction l 4b  interaction model

2. Common kinds of GLModels #3a  2 centered quant vars y’ = b 0 + b 1 x 1 + b 2 x 2 “X 1 ” is a centered quantitative variable X 1  X 1 – X 1mean “X 2 ” is a centered quantitative variable X 1  X 1 – X 1mean

3. Common kinds of GLModels #3a  2 centered quant vars y’ = b 0 + b 1 x 1 + b 2 x 2 b 0  mean of those in Cz with X=0 (mean) b 1  slope of Y-X 1 regression - slope same for all values of X 2  no interaction b 2  slope of Y-X 2 regression - slope same for all values of X 1  no interaction

4. 0 10 20 30 40 50 60 y’ = b 0 + b 1 X 1 + b 2 X 2 X 2 =0 +1 std X 2 -1 std X 2 -2 -1 0 1 2  X b 0 = ht of X 2mean line b 1 = slope of X 2mean line b 2 = htdifs among X 2 -lines X 2 -lines all have same slp (no interaction) 3a Xs are centered quant variables (both are standardized std = 1)

5. Common kinds of GLModels #3b  2 centered quant var & their product term/interaction y’ = b 0 + b 1 x 1 + b 2 x 2 + b 3 xz “X 1 ” is a centered quantitative variable X 1  X 1 – X 1mean “X 2 ” is a centered quantitative variable X 1  X 1 – X 1mean “XZ” represents the interaction of “X 1 ” and”X 2 ”

6. Common kinds of GLModels #3a  2 centered quant vars y’ = b 0 + b 1 x 1 + b 2 x 2 + b 3 xz b 0  mean of those in Cz with X=0 (mean) b 1  slope of Y-X 1 regression - slope same for all values of X 2  no interaction b 2  slope of Y-X 2 regression - slope same for all values of X 1  no interaction b 3  how slope of Y-X 1 reg lines change with X 2 value  how slope of Y-X 2 reg lines change with X 1 value

7. 0 10 20 30 40 50 60 y’ = b 0 + b 1 X cen + b 2 Z cen + b 3 XZ b0b0 b1b1 -b 2 Z=0 +1 std Z -1 std Z b2b2 Z cen = Z – X mean 3b 2 quantitative predictors w/ interaction (both are standardized std = 1) -2 -1 0 1 2  X cen a = ht of Z mean line b 1 = slope of Z mean line b 2 = htdifs among Z-lines X cen = X – X mean ZX = X cen * Z cen b3b3 b3b3 b 3 = slpdifs among Z-lines